J O U R N A L O F M A T E R I A L S S C I E N C E 3 6 (2 0 0 1 ) 1857 – 1861
Optical constants of the nano-crystal and polymer composite thin film PbTiO3/PEK-c Q. REN Department of Optics, Shandong University, Jinan 250100, People’s Republic of China; Optoelectronics Research Center, City University of Hong Kong, Hong Kong Y. T. CHOW Optoelectronics Research Center, City University of Hong Kong, Hong Kong F. Q. MENG, S. W. WANG National Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, People’s Republic of China Z. H. LU Department of Optics, Shandong University, Jinan 250100, People’s Republic of China C. B. MA, H. WANG, D. XU National Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, People’s Republic of China E-mail:
[email protected] W. A. GAMBLING Optoelectronics Research Center, City University of Hong Kong, Hong Kong Composite thin films of PbTiO3 nano-crystals and high transparency PEK-c polymer were prepared by spin coating. The size of PbTiO3 nanocrystals was evaluated to be 30–40 nm. The transparency spectra of PEK-c composite thin film in 360–800 nm were measured. The optical constants n, k of the film in the wavelength range 400–620 nm were investigated by the transmission spectrum. The dispersion of refractive index fits well to a three-term Sellmeier relation. At 633 nm wavelength the refractive index of PbTiO3 /PEK-c film was measured to be 1.6628 by a prism coupling method and showed a good agreement with C 2001 Kluwer Academic Publishers the calculated value using the Sellmeier relation. °
1. Introduction In recent years, the rapid development of optical communication and optical computation has brought about the development of the materials and devices for both photonics and photoelectronics. Glassy polymers doped with the electro-optic active units have significant nonlinear optical effect after poling by an electric field. They have great potential for waveguide applications in integrated optics and photoelectronics [1]. Lead titanate (PbTiO3 ) is a perovskite-type ferroeletric material. It has a high spontaneous polarization Ps (750 mC/m2 ) and a small relative dielectric constant εr (∼100). It also has high electro-optic coefficients. However, synthesis of large, perfect, and pure PbTiO3 single crystals is very difficult [2]. In our research, PbTiO3 nano-crystals were used as the nonlinear chromophores. The transparent polymer polyetherketone (PEK-c), which possesses a very high glass transition temperature and a low intrinsic dielectric coefficient, was selected as polymer host. By way of composition of the nano-crystals and polymer, it is hopeful to improve the stability of the electro-optic polymer materials and obtain materials with a high electro-optic figure C 2001 Kluwer Academic Publishers 0022–2461 °
of merit. A new high quality PbTiO3 /PEK-c thin film was prepared by spin coating technology. Because the optical constants of a composite film and their dispersion are important design parameters in fabrication of an optical coating, we measured the refractive index of the PbTiO3 /PEK-c composite film at 632.8 nm using the Metricon 2010 prism coupler with rutile prism and the transmission spectrum of it using a UV-VIS-NIR spectrophotometer. In this article, the composite refractive index n c of PbTiO3 /PEK-c polymer film has been studied in the wavelength range (400– 620 nm) by measuring the transmittance of the film. A calculation based on the method described in [3] was performed for deducing optical constants at different wavelengths.
2. Experiments and results 2.1. Preparation of PbTiO3 nano-crystals Nanocrystalline PbTiO3 has been synthesized by the chemical solution decomposition (CSD) technique. Firstly lead acetate trihydrate [Pb(CH3 COO)2 · H2 O] was dissolved in 2-methoxyethanol. Then titanium 1857
dissolved into chloroform, PbTiO3 was put into the solution, and the mixture was blended quite well using ultrasonic vibration. After the PbTiO3 was dispersed, the solution was directly deposited on a 1.06-mm-thick K18 glass substrate by spin coating at 2000 rpm for 40 s. Finally the film was put in a baking oven at 80◦ C for 30 min to remove residual solvent.
Figure 1 XRD pattern of PbTiO3 nano-crystals.
Figure 2 The TEM photograph of PbTiO3 nano-crystals.
butoxide [Ti(OC4 H9 )4 ] was added into the solution to form the PbTiO3 precursor solution under stirring. The mole ratio of Pb and Ti was selected to be 110 : 100. The solution was baked to vaporize the solvent, leaving PbTiO3 ultrafine precursor powder. Finally the dried powder was processed by rapid thermal annealing (RTA) at 700◦ C for 60 s and transformed into nanocrystalline PbTiO3 . The crystal structure of the microcrystals was identified by XRD with Cu Kα1 (λ = 0.15406 nm) radiation operated at 40 kV and 20 mA. Fig. 1 shows the XRD pattern of PbTiO3 powder. It conforms to the standard XRD pattern of PbTiO3 . The size of PbTiO3 microcrystals was evaluated by transmission electron microscopy (TEM: H-800 Hitachi). Fig. 2 is the TEM photograph of PbTiO3 microcrystals. The size of the PbTiO3 microcrystals is about 30–40 nm.
2.2. Preparation of PbTiO3 /PEK-c composite thin film The PbTiO3 /PEK-c composite films were prepared by spin coating. The weight ratio of PbTiO3 microcrystals to the polymer PEK-c is 20%. After the polymer was 1858
2.3. Measurement and calculation of optical constants The optical properties of a material may be represented by the refractive index n and the extinction coefficient k which are the real and imaginary parts of the complex refractive index n c = n − ik respectively. The refractive index n at 632.8 nm was measured firstly using a Metricon 2010 prism coupler with rutile prism. The measured value of the refractive index was 1.6628. The thickness value was obtained simultaneously, as 1.22 µm. Although the method possesses fine precision, only the refractive index of the film at 632.8 nm was measured. The measurement of the transmission spectrum of light through a thin absorbing film on a transparent substrate is sufficient to determine the real and imaginary parts of the complex refractive index, as well as the absorption coefficient α of the film. The method is used to determine n(λ) and α(λ) from the interference fringes of the transmission spectrum alone, provided the film sample is homogeneous and parallelfaced, the thickness d of the film is about a few microns. The effective bandwidth of the spectrophotometer is kept smaller than the half-width of the interference maximum. So an interference fringe pattern appears on the transmission spectrum of the thin film. The accuracy of the method is of the order of 1% [3]. A UV-VIS-NIR spectrophotometer (Lambda 19) was used for measuring the transmission spectrum of the film. The variation in transmittance T of PbTiO3 /PEK-c film with wavelength is shown in Fig. 3. We consider the extreme values of the transmission spectrum as the continuous functions of wavelength λ, corresponding to the envelopes of the maxima and the minima in the transmission spectrum. For a fixed wavelength, functions Tmax (λ) and Tmin (λ) give us the values of Tmax and Tmin . Then the refractive index of a film can be calculated by ¢1/2 ¤1/2 £ ¡ n = N + N 2 − n 20 n 21
(1)
where N=
n 20 + n 21 Tmax − Tmin + 2n 0 n 1 2 Tmax Tmin
where n 0 denotes the refractive index of air and n 1 denotes the refractive index of the transparent substrate at a given wavelength respectively. The variation in the refractive index n 1 with wavelength for the transparent substrate is shown in Fig. 4. Equation 1 shows that n at a given wavelength is explicitly determined from Tmax , Tmin , n 0 and n 1 at the same wavelength.
where £ ¤ (n + 1)(n 1 + n) 1 − (Tmax /Tmin )1/2 ¤ £ K = (n − 1)(n 1 − n) 1 + (Tmax /Tmin )1/2 The extinction coefficient k of a thin film is given by k=
λ α 4π
(4)
Knowing n and k, we are able to calculate the real and imaginary parts of the complex dielectric constant, εr and ε00 , using the equations: εr = n 2 − k 2
(5)
ε 00 = 2nk
(6)
The loss factor tan δ is given by tan δ =
Figure 3 Variation in transmission with wavelength for PbTiO3 / PEK-c film.
ε00 εr
(7)
We have calculated the refractive index n of the film at different wavelengths using Equation 1. The spectral dependence of the refractive index n for PbTiO3 /PEK-c film is shown in Fig. 5. The value of the refractive index n decreases with increasing wavelength. The dispersion of the refractive index for the PbTiO3 /PEK-c film was fitted to the three-term Sellmeier dispersion formula [4] n = A+
B C + 4 2 λ λ
(8)
where λ is in microns, A, B and C are the Sellmeier’s coefficients, and A is 1.68438, B is −0.01678, C is 0.003. At 633 nm wavelength the refractive index of PbTiO3 /PEK-c film was calculated to be 1.6612 using the Sellmeier relation. The thickness d of the thin film is calculated using Equation 2. The obtained value of d is 1.28 µm. The value of the refractive index n at 632.8 nm and the thickness d are
Figure 4 Variation in refractive index n 1 with wavelength for substrate.
The thickness d of a thin film can be calculated using the following equation: d=
Mλ1 λ2 2[n(λ1 )λ2 − n(λ2 )λ1 ]
(2)
where M is the number of oscillations between the two extrema; λ1 , n(λ1 ) and λ2 , n(λ2 ) are the corresponding wavelengths and indices of refraction. Knowing n and d, the absorption coefficient α of a thin film is calculated by the formula 1 α = − InK d
(3)
Figure 5 Variation in refractive index n with wavelength for PbTiO3 / PEK-c film.
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Figure 6 Absorption coefficient α against wavelength for PbTiO3 / PEK-c film.
Figure 7 Variation in extinction coefficient k with wavelength for PbTiO3 /PEK-c film.
consistent with the result of measuring by the Metricon 2010 prism coupler. The absorption coefficient α and the extinction coefficient k of the film are calculated using Equations 3 and 4 respectively. Figs 6 and 7 show the plots of α and k against wavelength for PT/PEK-c film. It is clear from Fig. 6 that the values of the absorption coefficient α for PT/PEK-c film are of the order of 103 cm−1 , that is the film is weakly absorbing. The calculation of the real part εr and imaginary part ε 00 of the complex relative dielectric constant of the thin film has also been made using (5) and (6). The variations in these two parameters with wavelength are shown in Figs 8 and 9. From these figures, we can see that the real part εr of the dielectric constant decreases with increasing wavelength. The loss factor tan δ of PbTiO3 /PEK-c film has been calculated using Equation 7 from the values of εr and ε 00 obtained above. The variation in the loss factor tan δ with wavelength is shown in Fig. 10. 1860
Figure 8 Real part εr0 of the dielectric constant as a function of wavelength for PbTiO3 /PEK-c film.
Figure 9 Imaginary part ε00 of the dielectric constant as a function of wavelength for PbTiO3 /PEK-c film.
Figure 10 Variation in loss factor tan δ with wavelength for PbTiO3 / PEK-c film.
3. Conclusions In conclusion, the composite thin films of PbTiO3 nanocrystals and high transparency polymer PEK-c were prepared. The size of PbTiO3 microcrystals was evaluated to be 30–40 nm by transmission electron microscopy. The new PbTiO3 /PEK-c polymer thin film is homogeneous and parallel-faced and shows good transparency. The transparency spectra in the range from 360 nm to 800 nm were measured. The greatest transmittance in this range is 80.7%. Because the value of T can be acquired to three significant figures, so the values of n, k, α, εr , ε 00 and tan δ are expressed to three significant figures also. It is demonstrated in our work that the very simple way of calculating the optical constants and their dispersion, is valid in the case of a weakly absorbing film surrounded by non-absorbing media.
Acknowledgements The authors acknowledge the financial support of the Chinese National Key Laboratory of Crystal Material, the National Natural Science Foundation and Shandong Province Natural Science Foundation of China.
References 1. R . F . S E R V I C E , Science 267 (1995) 1918. 2. K . L I J I M A , R . T O M I T A , R . T A K A Y A M A and L . U E D A , J. Appl. Phys. 60 (1986) 361. 3. R . S W A N E P O E L , J. Phys. E: Sci. Instrum. 16 (1983) 1214. 4. R . E . S T O I B E R and S . A . M O R S E , “Crystal Identification with the Polarizing Microscope” (Chapman & Hall, London, 1994) p. 292.
Received 18 July and accepted 27 September 2000
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